We have developed a quantification method that uses mainly room temperature rock magnetic measurements to calculate concentrations of ferrimagnetic particles in sediments. Our method uses saturation magnetization (Ms) as a total ferrimagnetic concentration proxy, the saturation remanence ratio (Mrs/Ms) as a magnetic grain-size proxy, the anhysteretic remanence ratio (χa/Mrs) to estimate inter-particle magnetostatic interactions, and the normalized susceptibility of the ferrimagnetic fraction (χf/Ms) to calculate the proportion of ultrafine, superparamagnetic particles. This approach eliminates the effect of dilution of the magnetic properties by weakly magnetic matter, and allows the calculation of direct concentrations (or fluxes for dated sedimentary profiles) of constituent ferrimagnetic components. We test our method on a short sediment core from an urban Minnesota lake, for which we calculate ferrimagnetic fluxes of four magnetic components, and compare their pre- and post-European settlement values. Our quantification technique can be applied for reconstructing past environmental changes in a range of sedimentary environments, and is particularly useful for large sets of samples, where detailed magnetic unmixing methods are unfeasible due to time or instrument constraints.
 Magnetic components (ensemble of particles with common origin, biogeochemical history, and a characteristic array of magnetic properties [Egli, 2004]) have been successfully modeled using magnetization spectrum methods, which exploit the subtleties of entire magnetization curves, reducing the non-uniqueness of a bulk parameter approach [e.g., Robertson and France, 1994; Roberts et al., 2000; Carter-Stiglitz et al., 2001; Kruiver et al., 2001; Heslop et al., 2002; Egli, 2003, 2004, 2006a; Egli et al., 2010]. However, the relatively involved methodology inherent to spectral techniques poses the disadvantage of only being able to process a limited number of samples in a given time span. On the other hand, bulk magnetic measurements are fast, inexpensive, non-destructive, and extremely sensitive to very small quantities of magnetic material, but they sometimes lack the ability to distinguish between different sedimentary magnetic components. For the analysis of large numbers of samples, such as typically encountered in long core studies, a technique that makes use of a limited number of spectral analyses on selected samples to calibrate numerous bulk measurements is particularly desirable.
 Several attempts have been made to quantify the concentration of various magnetic components using bulk parameters like χ, ARM, or IRM. Lees  has quantified the concentration of magnetic components in synthetic mixtures of up to six sedimentary sources by using linear modeling techniques, and has found χ to be the most reliable concentration-dependent parameter in case of complex mixtures. Large errors were encountered in the deconvolution of mixtures with a large number of components, implying that linearity does not apply for complex source mixing due to the extreme heterogeneity of considered samples, in addition to effects of magnetic viscosity of materials, interactions between particles, and inter-instrument calibration issues. In an attempt to unmix bulk χ measurements, von Dobeneck  introduced the concept of partial susceptibilities, which states that the bulk susceptibility of a sample is the sum of the susceptibilities of its constituent components. The method was subsequently developed in studies by Frederichs et al. , Xie et al. , Bleil and von Dobeneck , Funk et al. , and Xie et al. . The contribution of individual components to the bulk susceptibility is calculated via multiple regression, whereby each partial susceptibility term is related by a proportionality factor to the value of a magnetic parameter that is diagnostic for that particular component (e.g., ARM for fine-grained particles). The partial susceptibility method assumes linear proportionality between the susceptibility of the individual component and the magnetic parameter used as diagnostic, an assumption that does not always hold true. The method offers the advantage of reducing everything to susceptibilities, and the potential to eliminate the diagnostic parameter measurements if an empirical proportionality factor is universally found for every component considered in the model.
 The property of linear additivity of individual components that contribute toward a remanence parameter was used by Dunlop  in developing theoretical mixing curves of simple two-component numerical mixtures, based on hysteresis properties. Linear additivity of remanence was applied by Geiss and Zanner  to understand pedogenic enhancement in loessic soils in North American Great Plains. Bulk ARM and IRM measurements were used to quantify magnetite formed as a result of biogeochemical processes occurring in the topsoil. The pedogenic fraction obtained via this binary mixing model was found to underestimate calculations based on hysteresis parameter modeling, and coercivity spectra deconvolution. One reason for this discrepancy is their ARM-IRM model ignores the effects of magnetostatic interactions between particles in the sediment matrix, which tend to lower ARM values even for low ferrimagnetic concentrations [Egli, 2006b]. The decrease of ARM values as a result of inter-particle interactions was investigated by Yamazaki , who uses first-order reversal curve (FORC) diagrams in addition to bulk ARM and IRM measurements, and coercivity analysis of IRM acquisition curves to unmix sedimentary components in North Pacific sediment cores. The FORC analysis reveals the presence of a fine-grained non-interacting component, a fine-grained interacting component, and a coarse-grained background component. The concentration of the interacting particles is inversely related to the ARM ratio (ARM normalized by saturation IRM), indicating that interactions between particles are an important ARM-controlling factor. This is highly significant because the ARM ratio is widely used as a grain-size indicator in enviromagnetic studies. Since ARM is sensitive to magnetostatic interactions between proximal particles, the ratio can be artificially lowered if small particles occur in clumps, as is the case of collapsed bacterial magnetite chains, or clusters of pedogenic magnetite washed into a basin. Therefore, small-scale variations in the ARM ratio could point to interactions between particles rather than grain size changes, potentially offering information about the packing and arrangement of magnetic particles in the sediment matrix [Egli, 2006b; Kopp et al., 2006; Yamazaki, 2008].
 In this paper we present a quantification method that uses bulk rock magnetic measurements to calculate mass fractions, mass per volume concentrations, and mass fluxes of ferrimagnetic particles in sediments. Detailed rock magnetic and non-magnetic measurements are performed on representative samples to calibrate the modeling parameters. The quantification method consists of three parts: 1) Calculation of total ferrimagnetic concentration from in-field magnetization parameters, 2) Modeling the remanence-carrying fractions using remanent magnetizations to gain information about magnetic grain size and inter-particle interactions; this is tested on a selection of synthetic mixtures of stable single domain (SD), pseudo single domain (PSD), and multi-domain (MD) magnetite [Carter-Stiglitz et al., 2001; Dunlop and Carter-Stiglitz, 2006], and 3) Calculation of the superparamagnetic (SP) fraction from ferrimagnetic susceptibility and SP grain size distribution data. The quantification method is applied to a short sediment core from a Minnesota urban lake, but is applicable to a range of environments, including marine sediments, loess deposits, and soils.
2. Theoretical Considerations
2.1. Total Concentration of Ferrimagnetic Material
 Magnetic susceptibility, remanent magnetizations (ARM and IRM), and saturation magnetization are generally used to qualitatively assess the amount of magnetic material present in sediments. Saturation magnetization is an intrinsic property of magnetic materials, so should theoretically offer the most reliable concentration estimates. Susceptibility-based concentration estimates are widespread due to low cost and ease of measurement, but require information about magnetic mineralogy, grain size, and grain shape. Remanence measurements are accurate as concentration proxies only when magnetic composition is uniform (with respect to mineralogy and grain size) over the sedimentary interval investigated, because of the varying degree of remanence acquisition efficiency for different categories of magnetic particles. In this section we focus on χ and Ms, and discuss their use as ferrimagnetic concentration proxies.
2.1.1. Magnetic Susceptibility as a Ferrimagnetic Concentration Proxy
 Low-field magnetic susceptibility (χlf) is the most common magnetic property measured on sediments, popularized by the use of multisensor core loggers equipped with loop or point susceptibility meters [Nowaczyk, 2001]. Large-scale drilling expeditions employ the use of core loggers to measure unsplit sections of core immediately after retrieval for initial characterization of the sediments. At this stage χlf is mainly used to stratigraphically correlate between parallel cores from the same basin, and to roughly estimate the concentration of magnetic minerals in the core sections. χlf is strongly controlled by the presence of ferrimagnetic minerals, but this signature can be diluted by contributions of diamagnetic, paramagnetic, and antiferromagnetic materials [e.g., Dearing, 1999b]. Bulk χlf can be expressed as the sum of the magnetic contributions of all components to the total susceptibility signal:
where χi is the susceptibility of component i, and fi is the mass fraction of component i (Σfi = 1). This expression equates to the partial susceptibilities concept of von Dobeneck , but expressed in terms of fractions of pure substance susceptibilities. Since the ferrimagnetic component exerts the major control on χlf, its fraction (fferri) is of interest for calculating mass or volume based concentration parameters. In order to determine fferri, the contribution of diluting sedimentary matrix must be subtracted from the bulk value. Diamagnetic and paramagnetic substances have weak susceptibilities, but can amount to significant portions of bulk χlf if they are present in abundance, as in the case of water-laden, organic, carbonate-rich, or siliciclastic sediments [Rochette, 1987]. Susceptibility values for these substances are known from experimental work (see compilations by Hunt et al. [1995a] and Dearing [1999b]), and have average values of ∼−9 · 10−9 m3/kg for water and organic matter, ∼−8 · 10−9 m3/kg for calcite, ∼−6 · 10−9 m3/kg for feldspar and quartz, 0.1–7 · 10−6 m3/kg for paramagnetic and imperfect antiferromagnetic minerals. By comparison, ferrimagnetic mineral susceptibilities are on the order of 10−4-10−3 m3/kg. Mass fractions fi can be obtained from geochemical or mineralogical methods (e.g., loss on ignition (LOI), X-ray diffraction, etc.). After all non-ferrimagnetic contributions are determined and subtracted from χlf, equation (1) is reduced to:
where χf is the susceptibility corrected for non-ferrimagnetic contributions, and χferri is the susceptibility of the ferrimagnetic component. Average χferri values are 0.2–1.2 · 10−3 m3/kg for magnetite, 0.025–0.29 · 10−3 m3/kg for titanomagnetite, 0.3–0.5 · 10−3 m3/kg for maghemite, and 0.026–0.194 · 10−3 m3/kg for greigite [Hunt et al., 1995a; Dearing, 1999b; Peters and Dekkers, 2003]. For SP grains these values are expected to be one order of magnitude higher [Dunlop and Özdemir, 1997], because they have very high intrinsic susceptibilities, and are thermally unstable, thus being easily and efficiently magnetized even in small magnetic fields. They will dominate the χferri signal even when in low concentrations. The main challenge posed by the exercise of determining fferri from χf is finding an appropriate value for χferri, which implies some a priori knowledge about the ferrimagnetic mineralogy, grain size, and grain shape. Alternatively, if fferri can be determined from measurements of saturation magnetization, χferri can be calculated from equation (2). This scenario is discussed below.
2.1.2. Saturation Magnetization as a Ferrimagnetic Concentration Proxy
 Saturation magnetization Ms is an intrinsic property of a magnetic mineral, and provides a more straightforward measure of fferri than magnetic susceptibility. The only a priori information necessary for fferri calculation is knowledge of the ferrimagnetic mineralogy. Ferrimagnetic mass fraction is calculated as:
where bulk Ms is obtained from hysteresis measurements after correcting for high field non-ferrimagnetic contributions, and μferri is the ferrimagnetic saturation magnetization, which can be written as a linear combination of the saturation magnetizations of the ferrimagnetic constituents:
where pj is the fraction of total ferrimagnetic mass represented by component j (Σpj = 1) and μj is its intrinsic mass-normalized saturation magnetization. Ferrimagnetic mineral composition can be determined either from magnetic or non-magnetic methods. Magnetic methods are based mainly on thermal order-disorder transitions (Curie or Néel points) or spin reorientations and are semiquantitative, while non-magnetic methods, such as Mössbauer spectroscopy and X-ray diffraction on magnetic extracts, permit a direct calculation of the ferrimagnetic mineral fractions. The main ferrimagnetic minerals found in lake and marine sediments are magnetite (μMt = 92 Am2/kg), maghemite (μMh = ∼74.3 Am2/kg) [Dunlop and Özdemir, 1997], and greigite (μGr = ∼59 Am2/kg) [Chang et al., 2008]. Magnetite and maghemite are by far the most common, so in the absence of reliable methods of ferrimagnetic mineral determination, calculating concentrations both as magnetite and maghemite will set the concentration interval boundaries, assuring accuracy of results, although at the expense of reduced precision.
 The slope correction applied to raw hysteresis loop measurements also offers an alternative way to determine the contribution of non-ferrimagnetic components to χlf, bypassing the need for sediment composition information. The high field susceptibility χhf is calculated from the slope of a loop at magnetic fields larger than the saturating field, which is typically a few hundred mT for important ferrimagnets, and is equivalent to the sum of partial susceptibilities of all non-ferrimagnetic components contributing of χlf. The ferrimagnetic contribution to χlf can thus be expressed as:
Having calculated fferri and χf (from equations 3–5), χferri can now be obtained from equation (2). This is done in order to calculate the SP particle fraction contributing to the total ferrimagnetic concentration (see section 2.3).
2.1.3. Expression of Total Ferrimagnetic Concentration
 The fraction of ferrimagnetic material is in effect a mass concentration, i.e., the mass ferrimagnetic component of total sediment mass. Since ferrimagnetic concentrations are on the order of thousandths of the total sediment mass, it is more convenient to express fferri as a part per thousand (ppt, mg/g, g/kg, etc.) concentration:
The concentration of ferrimagnetic minerals can also be expressed as mass ferrimagnetic material per unit volume sediment:
where Cferri is the total ferrimagnetic concentration as mass per volume unit, ρwet is the wet sediment density, and fsed is the mass fraction sediment (i.e., the ratio of dry mass to wet mass). Wet sediment density is a standard parameter measured during initial core logging, but can also be calculated on samples of known volume by dividing the wet mass of a sample by its volume. If sample volume is unknown, ρwet can be obtained from compositional analysis (e.g., LOI) as a sum of pure substance densities (e.g., 1000 kg/m3 for water) weighed by their respective mass fractions. Cferri is of interest for calculating ferrimagnetic particle fluxes in sediment cores with established chronologies. The mass flux of ferrimagnetic material ferri to the sediment column is obtained from multiplying Cferri by the sediment accumulation rate Rsed (expressed in length units per time):
In order to separate the fluxes of various ferrimagnetic components, an unmixing method is necessary.
2.2. Concentration of Remanence-Carrying Ferrimagnetic Components
 In this section we present a three-component mixing model that makes use of bulk remanence measurements to quantify the remanence-carrying fractions of fferri. Unmixing models using either hysteresis or bulk remanence parameters have been used to analyze synthetic, natural, and numerical mixtures of two components, and are based on the linear additivity of remanence properties when the mixture is monomineralic [Dunlop, 2002; Dunlop and Carter-Stiglitz, 2006; Geiss and Zanner, 2006]. The mixing model presented here combines the remanence aspect of the hysteresis approach of Dunlop  and Dunlop and Carter-Stiglitz  with the ARM-IRM modeling of Geiss and Zanner . However, we use the ARM ratio primarily to evaluate particle interactions rather than grain size, essentially extending two-component models to mixtures of three end-members, here MD (including PSD), uniaxial non-interacting SD (UNISD) [Egli et al., 2010], and interacting SD (ISD). Our model accounts for all the remanence-carrying contributors to fferri, i.e., the non-SP ferrimagnetic fraction.
 Bulk ARM and saturation IRM (or Mrs) values can be written as linear combinations of the ARM and Mrs values of the mixture end-members. Since the absolute remanence values of end-member components are not invariant, they are normalized by Ms (μferri is constant across the mixture) in order to obtain comparable ratios. The resulting system of equations for the three-component (MD, UNISD, and ISD) mixing model is:
where χa is the ARM susceptibility (ARM normalized by acquisition bias field), (Mrs/Ms)bulk and (χa/Ms)bulk are ratios obtained from measured parameters, (Mrs/Ms)i and (χa/Ms)i are the respective ratios of end-member i, and gi is the fraction of component i. The system is solved for gi. Since χa/Ms is not a commonly used ratio, the second equation in (9) can be divided by the first in order to obtain the expression for the ARM ratio (χa/Mrs). The system then becomes:
Note that ARM and Mrs combine in a nonlinear fashion. Theoretical values for Mrs/Ms and χa/Mrs can be predicted by varying the end-member fractions gi over the interval [0, 1] with the third condition of the system always satisfied. The model ratio values can be plotted in Mrs/Ms versus χa/Mrs scatter diagrams at regular gi intervals (e.g., 0.1) as “mixing grids,” and overlain with the experimental values for comparison. The mixing grids are equivalent to ternary diagrams in gi coordinates. The choice of end-member ratios will be discussed in section 4.
2.3. Concentration of Superparamagnetic Particles
 In order to calculate the absolute concentrations of the remanence-carrying components, the SP concentration must be first subtracted from the total ferrimagnetic concentration. Rearranging equation (2) to solve for χferri, and substituting fferri with Ms/μferri (equation 3), we find that χferri is nothing but a multiple of χf/Ms, where the multiplier is the ferrimagnetic saturation μferri. The ratio χf/Ms has been used in a quantitative way to express fluctuations in high susceptibility SP grains relative to a non-SP baseline for Chinese loess plateau deposits [Hunt et al., 1995b]. SP concentrations obtained this way were found to be in good agreement with concentrations calculated via the more reliable thermal demagnetization of low temperature remanence method [Hunt and Banerjee, 1992], and are much easier to perform. The non-SP susceptibility (χnonSP), carried by SD and MD grains, has values an order of magnitude lower compared to the typical susceptibility of SP particles (χSP). χferri can be written as the linear combination of χSP and χnonSP, an expression which can be rearranged to solve for the SP fraction (fSP):
χnonSP is typically characterized by a narrow range of values (0.4–0.8 · 10−3 m3/kg for magnetite [Dunlop and Özdemir, 1997]), while χSP can be determined using information about the SP grain size distribution. For very small particles (<10 nm) the relationship between χSP and particle volume is linear at room temperature, according to Néel  theory of thermally activated magnetization. Larger SP particles (10–20 nm) exhibit frequency dependence of susceptibility at room temperature, because their magnetization relaxation times are comparable to the observation times of the experiment. Worm  has investigated the nature of the SP-SD transition and the behavior of the magnetic susceptibility across this boundary. The relationship between χSP and particle volume is no longer linear, and the transition to SD susceptibilities is gradual, especially if the particles are characterized by a distribution of coercivities [see Worm, 1998, Figure 2]. In Worm's  approach, frequency-dependent susceptibility measurements across a range of temperatures are necessary to estimate the SP particle size distribution, and thus χSP (which for magnetite is found to have values of up to 8 · 10−3 m3/kg). The choice of χSP depends from case to case and will be discussed in context in Section 4.
3. Materials and Methods
3.1. Samples and Non-magnetic Treatments
 The synthetic mixtures used for testing our remanence model (Section 2.2) have been prepared by Carter-Stiglitz et al.  by combining an SD end-member with PSD and MD end-members in incremental mass fractions. The SD particles are freeze-dried cells of vibroid magnetotactic bacterium MV1, which produces prismatic magnetite magnetosomes with mean volumes of 0.65 · 10−22 m3 and aspect ratios of 1.5, aligned in linear chains (samples from the same batches have also been used by Moskowitz et al. ). The PSD and MD phases are Wright Company magnetites 3006 and 041183 with grain sizes of 1.06 ± 0.71 μm and 18.3 ± 12 μm respectively [Yu et al., 2002]. The non-SD component was first dispersed in CaF2 using a blender; the MV1 freeze-dried cells were then added in the desired mixing proportions, and gently mixed together using a mortar and pestle [Carter-Stiglitz et al., 2001].
 The natural samples used in this study are lacustrine sediments from Brownie Lake, a small urban water body in Minneapolis, Minnesota. Brownie Lake has a surface area of ∼5 · 104 m2 and a maximum depth of 14.1 m (5.6% relative depth). The lake has been meromictic (permanently stratified) since the lake level was artificially lowered by ∼3 m in 1917 [Swain, 1984; Tracey et al., 1996]. A 139 cm core was retrieved in 2007 from 13 m water depth, using a drive-rod surface corer. The core was logged and described at the University of Minnesota Limnological Research Center, and sampled at a resolution of 1 cm. Aliquots of ∼1 cm3 were used for LOI analysis, according to the procedure described by Dean  and Heiri et al. . Separate subsamples were freeze-dried, weighed, and packed in plastic boxes for magnetic analyses. On 15 September 2009 a water column profile of dissolved oxygen (DO) was recorded using a Hydrolab multisensor probe. Water samples were collected using a Van Dorn sampler at a resolution of 0.5–1 m across the oxic-anoxic interface (OAI) and 1–1.5 m below the OAI. Between 150 and 200 ml of each sample were filtered in the laboratory using 0.1 μm filters, which were then frozen and packed in plastic straws. A surface sediment (top 10–15 cm of the sediment column) sample was collected on the same date from a water depth of 13.5 m using an Ekman dredge. A subsample was disaggregated with sodium hexametaphosphate (0.5 g to 100 ml sediment slurry) and circulated through an in-house magnetic separator. The magnetic fraction was extracted using a high-gradient permanent magnet, collected on a daily basis for a two-week period, and stored in isopropanol at 4°C. The extract was then dried at 25°C for 24 h, and used for room temperature 57Fe Mössbauer spectroscopy. Mössbauer analysis was performed with a conventional constant-acceleration spectrometer in transmission geometry with a source of 57Co in an Rh matrix. Hyperfine parameters such as magnetic hyperfine field (BHF), isomer shift (IS) and quadrupole shift (QS) have been determined by NORMOS program [Brand, 1987], and α-Fe at room temperature was used to calibrate isomer shifts and velocity scale.
3.2. Magnetic Measurements
 All magnetic measurements were performed at the University of Minnesota Institute for Rock Magnetism. Magnetic susceptibility was measured on a Kappabridge KLY-2 susceptometer operating at a frequency of 920 Hz. A D-Tech 2000 demagnetizer was used for ARM acquisition, which was imparted in a 0.1 mT steady field superimposed on an AF field decaying from a peak value of 200 mT, with a rate of 5 μT per half cycle. Stepwise alternating frequency (AF) demagnetization of the ARM was performed on the filtered water samples using an automated 2G Enterprises superconducting quantum interference device (SQUID) magnetometer, with peak fields increasing from 0.5 to 170 mT. The demagnetization procedure contains one hundred measurement steps spaced on a logarithmic scale. IRM was imparted on the same samples by pulsing the samples in a 200 mT field using a 2G core pulse magnetizer. This was done two times in order to remove any viscous effects. The IRM was demagnetized following the same procedure as for the ARM. For coercivity component analysis, first derivatives of the demagnetization curves were fitted with skewed generalized Gaussian distributions using MAG-MIX [Egli, 2003]. Hysteresis loops were measured on a Princeton Measurements vibrating sample magnetometer using a maximum applied field of 1 T. The loop slopes at high fields (>0.7 T) were used to correct raw Ms values, and to calculate the contribution of non-ferrimagnetic minerals to low field susceptibility. A Quantum Design magnetic properties measurement system (MPMS-2) was used to perform low temperature demagnetization experiments on representative lake sediment samples. Thermal demagnetization of saturation IRM (SIRM) acquired at 10 K in a 2.5 T field after cooling the sample in zero magnetic field (the so-called ZFC treatment) was measured from 10 K to room temperature at 5 K intervals. Room temperature SIRM imparted in a 2.5 T field was partially decayed by cooling the sample to 10 K and rewarming it back to 300 K. Measurements were performed in zero field at 5 K intervals. The MPMS was also used to measure susceptibility as a function of temperature and frequency on the selected lake samples. AC susceptibility was measured in 10 K steps from 10 to 300 K at frequencies of 1, 10, and 100 Hz.
4. Results and Discussion
4.1. Synthetic Mixtures
 We use the synthetic samples of known end-member proportions to test the validity of our mixing model defined by system (9). The Mrs/Ms and χa/Mrs values of the SD-MD and SD-PSD mixtures are plotted in Figure 1a, together with theoretical values for mixture bulk ratios determined from varying gi in (10). The measured values fall on the PSD-SD and MD-SD mixing lines (i.e., two-component mixtures; g3 = 0), where the SD end-member ratio values are Mrs/Ms = 0.498, and χa/Mrs = 1.6 · 10−3 m/A. For comparison, Moskowitz et al.  measured ARM ratios on freeze-dried MV1 cells and obtained values of 1.8–2.1 · 10−3 m/A, while Kopp et al.  report ARM ratios of 1.59–1.79 · 10−3 m/A for intact and treated (with sodium dodecyl sulfate and/or ultrasonication followed by dilution in sucrose) freeze-dried MV1 cells. Moskowitz et al.  have also performed ARM acquisition experiments on wet MV1 cell suspensions fixed with 1% glutaraldehyde, and obtained ARM ratio values of 3.1–3.5 · 10−3 m/A. Fragile bacterial cell membranes must be partially ruptured or destroyed in the process of freeze drying, which involves freezing the sample and extracting the water fraction by sublimation in vacuum. The partial destruction of the cell membranes results in magnetosome chain clumping, which explains the lower ARM ratios of freeze-dried samples as the effect of interactions between the disturbed magnetosomes. Transmission electron microscope (TEM) analysis of the untreated, freeze-dried MV1 samples of Kopp et al.  reveals that only about 10% of the magnetosomes are isolated from other crystals and chains, while the bulk of the chains are either in side-to-side arrangements, or collapsed into loop configurations [Kopp et al., 2006, Figure 2a]. Given the ARM ratio value of 1.6 · 10−3 m/A for the SD end-member component in our mixtures, we conclude that the SD end-member physically added to the mixtures is in fact a combination of non-interacting and interacting particles and chains, which means the synthetic samples can be modeled as mixtures of three components.
 We first assign values to the remanence ratio (Mrs/Ms) and ARM ratio of the non-interacting SD end-member. For magnetite, Mrs/Ms has a value of 0.5 by definition of randomly oriented UNISD particles [Stoner and Wohlfarth, 1948]. The determination of the value for the ARM ratio is not as clear-cut. Egli and Lowrie  have developed an analytical solution for the ARM of assemblages of UNISD particles, and have found that the ARM ratio of UNISD grains characterized by uniform rotation depends chiefly on grain size and grain shape, and only weakly on microcoercivity. They calculate a maximum χa/Mrs value of 3.7 · 10−3 m/A for prismatic crystals with volumes of 1.25–2.2 · 10−22 m3, and aspect (length to width) ratios of 1.43–2.5 [see Egli and Lowrie, 2002, Figure 11c]. Mean volumes of 0.65 · 10−22 m3 and aspect ratios of 1.5 (as is the case with our MV1 samples) yield ARM ratios of ∼2 · 10−3 m/A according to the Egli and Lowrie  model, and yet χa/Mrs values obtained from wet suspensions of the same batches of particles used in this study [Moskowitz et al., 1993] are close to the maximum values predicted by theory. This discrepancy can be explained by the fact that Egli and Lowrie  model randomly oriented non-interacting isolated particles, and not magnetosome chains. The arrangement of particles in linear chains should have the same effect as particle elongation, namely to increase dipole moment and coercivity. The increase in chain magnetic moment would lead to a higher chain ARM ratio than that of its isolated magnetosomes. Therefore having a UNISD end-member with a χa/Mrs value of 3.7 · 10−3 m/A is not an unreasonable assumption.
 The ISD end-member ratios (Mrs/Ms = 0.497 and χa/Mrs = 0.47 · 10−3 m/A) were determined so that a) Mrs/Ms of the 100% SD mixture would fall on the ISD-UNISD mixing line; b) the correlation between the (non) SD fraction added to the mixture and the inverted (non) SD fraction obtained from the solution to system (9) approaches a 1:1 relationship (i.e., the slope of a linear fit to the data is close to 1); and c) Pearson's correlation coefficient R of the fits for each mixture is maximized (R = 0.999, Figure 1c). The ARM ratio of the ISD end-member is close to the value of 0.41 · 10−3 m/A measured by Kopp et al.  on ultrasonicated MV1 cells diluted at 1 ppt in sucrose (their sample V2a). The ultrasonic treatment destroys the bacterial cell membrane but keeps the magnetosome organelles intact, while the dilution prevents the particles from clumping. TEM images of V2a show collapsed chains throughout, but there are no major magnetosome clumps, and some of the particles remain isolated [Kopp et al., 2006, Figure 2b]. According to the calculations of Egli [2006b] this corresponds to an average spacing of three particle diameters. The SD component of our mixtures is therefore a combination of intact chains and isolated magnetosomes (the UNISD end-member), and collapsed chains of particles that still preserve their magnetosome membranes (the ISD end-member). The mixing grids between the three end-members are calculated using system (10), but we plot only the outer contours of these grids (continuous lines Figure 1a) in order not to unnecessarily clutter the diagram. For reference, a similar mixing grid, calculated at fraction increments of 0.1, is plotted in Figure 5a. We find that the ISD component in our synthetic samples comprises 60–75% of the total SD grains in the mixtures (shaded area in Figure 1b), compared to the 90% visual estimate of Kopp et al.  from TEM analysis of samples with equivalent ARM ratios.
4.2. Lake Sediments
4.2.1. Sedimentary Units and Chronology
 European settlement in the Brownie Lake area began shortly after 1850. In the core it is expressed as a change in sedimentary characteristics at a depth of 65 cm, marking the boundary between the post-settlement sedimentary succession (Unit 1) and the pre-settlement sediments (Unit 2). Unit 1 (0–65 cm; ca. 1850-present) is a laminated clayey silt with authigenic calcite and diatoms. The laminae are discontinuous, and of variable thickness of up to 0.5 cm. Organic matter (mostly sapropel) and carbonate contents each average between 10 and 20% of the dry sedimentary matter. A tan sandy layer that occurs at 50 cm marks an artificial lowering of the water level in 1917, the year a canal connecting Brownie Lake with Cedar Lake to the south was completed. Unit 2 (65–140 cm; <1850) is a dark brown, massive, partly humic peat composed of terrestrial mosses and aquatic plants. Organic matter fluctuates between 30 and 60%, while carbonate content is constant at ∼5%. The chronology of the Brownie Lake core is based on the correlation with the 210Pb dated core of Swain . The correlation is drawn from organic matter concentration variations, and is aided by the recognition of marker horizons such as the 1917 sand lens.
4.2.2. Room Temperature Magnetic Properties
 Sediment-magnetic properties of the Brownie Lake core are presented in Figure 2, and the mean (m) and standard deviation (σ) of each parameter are listed for both sedimentary units in Table 1. The standard deviation was calculated for the detrended magnetic parameters, in order to remove variability introduced by long-term shifts in mean. In Table 1 is also computed the coefficient of variation (CV = σ/m) for each magnetic parameter within a sedimentary unit. The concentration-dependent parameters χlf, χa, Mrs, and Ms show higher variability in Unit 1 compared to Unit 2 (higher CVs), and a general increase in values with the decrease in depth in core over the past 150 years. In Unit 2 the concentration-dependent parameters exhibit a larger shift in mean to lower values, but the detrended variance is lower, indicating a steady decrease in concentration with time, up to the European settlement horizon. The concentration-independent magnetic parameters Mrs/Ms, χa/Mrs, and χf/Ms have weak increasing trends with decreasing depth in Unit 1. In Unit 2 Mrs/Ms and χa/Mrs have weak decreasing trends and lower variability than in Unit 1 (lower CV values), while χf/Ms has a weak increasing trend and slightly higher variability.
Table 1. Mean, Standard Deviation, and Coefficient of Variation Values for the Magnetic Properties of Brownie Lake Sediment Unitsa
Here, m is the mean, σ is the standard deviation, and CV = σ/m is the coefficient of variation. Standard deviations are calculated after subtracting the effect of any long-term trends on the magnetic parameters. CV is a unitless measure.
χlf (10−7 m3/kg)
χa (10−5 m3/kg)
Mrs (10−3 Am2/kg)
Ms (10−3 Am2/kg)
χa/Mrs (10−3 m/A)
χf/Ms (10−5 m/A)
4.2.3. Suspended Sediments
 ARM and IRM profiles of the water filtrates are shown in Figure 3a, along with the DO profile. Oxygen concentrations are close to saturation values in the epilimnion (7.6–8 mg/l), but then decrease to 0.2 mg/l at 4m, with a maximum gradient between 2.5 and 3 m. At the depth of 3 m DO = 1.3 mg/l, and both ARM and IRM values are lowest in the profile. DO drops to 0.75 mg/l between 3 and 3.5 m, with a simultaneous increase in ARM and IRM, which reach maximum values at 4m, immediately below the OAI. Below 4 m oxygen levels remain low, with a slight increase from 0.2 to 0.35 mg/l in the bottom waters. ARM and IRM are still elevated at 5 m, but decrease significantly below 5 m. The ARM ratio peaks (2.6–2.7 · 10−3 m/A) at the OAI (3.5–4 m), is lowest (<1 · 10−3 m/A) between 7 and 9 m, and has values of 1–1.5 · 10−3 m/A for the rest of the filtrates.
 The biogenic contribution to both ARM and IRM was separated by coercivity component analysis from first derivatives of ARM and IRM demagnetization curves, using the fitting model proposed by Egli [2003, 2004]. Figure 3b shows three coercivity components present below the OAI, each defined by two distribution parameters: median coercivity and dispersion. According to the definitions of Egli  the low coercivity component comprises large detrital grains, and fine extracellular particles mediated by dissimilatory microorganisms (D); the intermediate coercivity component is identified as biogenic “soft” (BS), and the high coercivity component as biogenic “hard” (BH). The ARM ratio of each component is plotted in Figure 3c. The two biogenic components have maximum ARM ratios at the OAI (3.4 · 10−3 m/A for BS; 3.82 · 10−3 m/A for BH). Below the OAI BS decreases to <1 · 10−3 m/A at 8 m (where BH peaks at 3.2 · 10−3 m/A), and increases again toward the bottom (where BH < 1 · 10−3 m/A). Integrating BS and BH remanences over the entire water column profile, we obtain average ARM ratios of 2.44 · 10−3 m/A for component BS, and for 2.13 · 10−3 m/A for component BH. The ARM and IRM values of the two biogenic components were respectively added for each sample in order to calculate an average biogenic ARM ratio (BS + BH in Figure 3c). At the OAI the ARM ratio of BS + BH is 3.47 · 10−3 m/A, while its integrated value over the water column is 2.36 · 10−3 m/A.
4.2.4. Total Ferrimagnetic Concentration
 To calculate the total mass concentration of ferrimagnetic particles in a particular sample using equation (3), the nature of the ferrimagnetic carrier must first be identified. The low temperature magnetization experiments reveal the presence of partially oxidized magnetite in both sedimentary units, with more pronounced maghemitization in Unit 2. Zero field cooled (ZFC) 10 K SIRM warming curves of typical samples for each sedimentary unit are shown in Figure 4a. The Unit 1 sample demagnetization rate is highest between 10 and 50 K, where ∼30% of the SIRM is lost, decreases between 50 and 100 K (10% loss), increases again (20% loss) between 100 and 130 K through the Verwey transition (TV), and is lowest between 130 and 300 K, interval in which only 10% more is lost. The remanence retained at room temperature is a little over 30%. By comparison, the Unit 2 sample memory is almost double. The initial remanence loss of this sample is steep but the magnitude of loss (∼20%) is less than in Unit 1. This is followed by a decrease in demagnetization rate with a broad (10% loss over 30K) but still distinct TV, shifted to lower temperatures (80–110 K). Above TV the demagnetization rate remains constant at ∼7% per 100 K. The depressed and broadened TV, shifted to lower temperature is a trait of non-stoichiometric magnetite, while remanence loss below and above TV have also been attributed to magnetite oxidation in well characterized starting material [Özdemir et al., 1993]. The degree of oxidation also dictates the magnitude of the demagnetization rate below and above TV. The initial remanence loss is thus highest for surface oxidized magnetite particles, while severely maghemitized particles demagnetize at a higher rate above TV [Özdemir and Dunlop, 2010]. However, this remanence loss can also occur due to unblocking of magnetite SP particles during sample warming. To avoid the effect of superposition of the two phenomena, we examine the behavior of room temperature remanence during low temperature cycling (Figure 4b). Typical Unit 1 curves show a 1% increase in remanence with cooling from 300 to 250 K, followed by a loss of ∼25% to TV, and only a slight increase in remanence at temperatures lower than 70 K. The cooling curve is reversible from 10 to 60 K, temperature above which the remanence recovery is incomplete. Above TV, the warming curve peaks around 170 K, followed by a steady decrease to room temperature. The total remanence recovery is above 75%. The Unit 2 cooling curve shows the same magnitude increase in remanence between 300 and 250 K, but is followed by a gradual decrease to 110 K corresponding to a remanence loss <2%. Below TV there is a ∼2% increase in remanence, which is reversible upon warming from 10 to 100 K. Above 100 K it steadily decreases to room temperature, first gradually to ∼250 K and then more steeply from 250 to 300 K. Compared to the Unit 1 sample, only 5% of the room temperature SIRM is lost in the low temperature cycling process. According to Özdemir and Dunlop  the hump-shaped cooling and warming curves above TV, together with the high degree of room temperature remanence memory are diagnostic for magnetite in the advanced stages of maghemitization. Özdemir and Dunlop  have also proposed a semiquantitative method for estimating the oxidation parameter z [O'Reilly and Banerjee, 1967; Readman and O'Reilly, 1971], by comparing the room temperature memory loss (ΔMc) with the difference in magnetization between 20 K and TV (ΔMm). Although this method has not been extensively tested on a range of particle size fractions (or mixtures thereof), it can be useful as a first-pass estimate of the degree of maghemitization [Özdemir and Dunlop, 2010]. In our case, Unit 2 ΔMc and ΔMm values fall in the range of PSD magnetite characterized by z values of 0.8–0.9, whereas in Unit 1 the small ΔMm value, determined by the predominance of a low coercivity MD component [Muxworthy et al., 2003], does not allow a comparison.
 The room temperature Mössbauer spectrum of the surface sediment magnetic extract (Figure 4c) gives us a quantitative measure of maghemite concentration for Unit 1 in this case. The fitted parameters correspond to the sextets of hematite, maghemite, site A (tetrahedral) and site B (octahedral) of magnetite, and doublets of Fe2+ and Fe3+ (Figure 4c and Table 2). The BHF of site A and B of magnetite, maghemite and hematite are in agreement with values from the literature and suggest iron phases without presence of foreign elements (e.g., Ti or Al substitutions) in their structure [Murad and Cashion, 2004]. However, the magnetite site A/site B concentration ratio (Table 2) is higher than 0.5, showings some deviation from a stoichiometric form. The non-stoichiometry is interpreted as the combined effect of a stoichiometric magnetite core, a non-stoichiometric magnetite transition zone (characterized by a distribution of z), and an outer maghemite shell. The Fe2+ doublet is associated with paramagnetic minerals (e.g., iron phyllosilicates), and the Fe3+ doublets correspond to paramagnetic iron minerals (wide Fe3+ doublet), as well as to superparamagnetic iron oxides (narrow Fe3+ doublet). If we consider only the magnetically ordered ferrimagnetic particles, then 91% of the iron is in contained in non-stoichiometric magnetite, and 9% is in maghemite. If we assume the SP fraction is entirely ferrimagnetic (i.e., no ferrihydrite) and fully oxidized, then only 81% of the iron is in contained in non-stoichiometric magnetite, and 19% is in maghemite. Since ΔMc of Unit 1 samples is ∼0.25, the average remanence ratio is 0.16 ± 0.02 (characteristic of generic PSD behavior), and room temperature SIRM memory is partially due to SD grains, an upper limit for z can be set at 0.5 for Unit 1, based on the model of Özdemir and Dunlop . The Mössbauer-based calculation helps lower this upper limit to 0.3. The oxidation parameter is necessary for determining μferri values for Units 1 and 2 from equation (4), where the two components considered are magnetite (μMt = 92 Am2/kg) and maghemite (μMh = 74.3 Am2/kg), and the weighing factor is none other than z, according to the quasi-linear relationship between z and either end-member fractions of the magnetite-maghemite oxidation series [Readman and O'Reilly, 1972]. For Unit 1 we find an average ferrimagnetic component with μferri = 88 Am2/kg (corresponding to z = 0.3), while for Unit 2 the average μferri = 78 Am2/kg (z = 0.8). The total mass concentration of ferrimagnetic material (cferri) is obtained by normalizing bulk Ms measurements by the respective μferri value (equation 3). Figure 4d shows cferri delimited by total ferrimagnetic mass concentration calculated as magnetite (lower limit) and maghemite (upper limit).
Table 2. Magnetic Hyperfine Parameters at Room Temperature for the Brownie Lake Surface Sediment Magnetic Extract
4.2.5. Concentration of Remanence-Carrying Particles
 The sedimentary MD, UNISD, and ISD components are modeled using system (9), which has been successfully tested on the synthetic mixtures. The choice for end-member component ratios is driven by the characteristics of the end-member components in the depositional environment examined.
 The UNISD component comprises all SD particles or chains of particles that are isolated from other magnetic grains in the sediment matrix. These particles can have various sources, but in lake sediments they are overwhelmingly biogenic [Egli et al., 2010]. Lakes generally have diverse magnetotactic bacteria communities that live in specific geochemical conditions [Moskowitz et al., 2008], so it is expected that populations of magnetosomes originating in different environmental stress zones have characteristic magnetic properties, specifically the ratios used in this model. The magnetosomes present in our samples have been identified as non-stoichiometric magnetite, based on the Mössbauer analysis and the presence of Verwey transition in the low-temperature experiments. The remanence ratio of the UNISD component is therefore set to 0.5 [Stoner and Wohlfarth, 1948]. The ARM ratio should reflect the average value of non-interacting magnetosomes and chains from all bacterial strains. Since it is difficult to identify all the species that produce magnetosomes in natural samples, and there is little data for wild strain magnetic properties, the choice of UNISD ARM ratio should be based on measurements of samples collected from the horizons inhabited by magnetotactic bacteria. The Brownie Lake water column ARM ratio of the integrated biogenic coercivity component peaks at the OAI (BS+BH in Figure 3c). The decrease of the ARM ratio with depth is partially due to the incipient breakdown during settling of some of the chains produced at the OAI, and partially due to possibly lower intrinsic ARM ratios of magnetosome chains produced by some of the strains in the low-oxygen layers [Egli, 2004]. It is also plausible that some of low coercivity particles are non-interacting pedogenic particles that also have lower intrinsic ARM ratios [Geiss et al., 2008]. Coercivity spectra deconvolution does not discriminate between interacting and non-interacting particles, but isolating the biogenic component in its immediate environment is the most important step in the process of choosing a representative ARM ratio for UNISD. Based on the BS+BH ARM ratio value at the OAI, the habitat of magnetotactic bacteria, we use (χa/Mrs)UNISD = 3.5 · 10−3 m/A in our model. The ISD end-member ratios were chosen to represent strongly interacting SD particles (Mrs/Ms = 0.41; χa/Mrs = 0.12 · 10−3 m/A [Moskowitz et al., 1993]), e.g., clumps of collapsed magnetosomes from bacterial cells with totally degraded organic membranes, or washed-in pedogenic particle aggregates. The MD component end-member ratios (Mrs/Ms = 0.05; χa/Mrs = 0.1 · 10−3 m/A) represent average values for MD grains sensu lato (i.e., account for the presence PSD particles).
Figure 5 illustrates the modeling results. Bulk Mrs/Ms and χa/Mrs are compared to theoretical values in Figure 5a. A mixing grid is formed by the lines connecting the three end-member components (defined above), which are calculated using system (10). The fractions of the end-members in each sample are plotted in a ternary diagram (Figure 5b), which is equivalent to the mixing grid, but in gi coordinates. On average, Unit 1 samples contain 60–80% MD, 20–30% ISD, and <10% UNISD particles. Comparatively, pre-settlement samples contain only 30–50% MD grains, while ISD and UNISD end-members are well represented with 20–40% of the total ferrimagnetic mass each. In Figure 5c we plot results from eight model runs that used all possible combinations of the following end-member ratio pairs (Mrs/Ms, χa/Mrs), which represent boundaries defined for each component: (0.5, 3 · 10−3 m/A) and (0.5, 4 · 10−3 m/A) for UNISD, (0.41, 0.1 · 10−3 m/A) and (0.45, 0.15 · 10−3 m/A) for ISD, (0.01, 0.05 · 10−3 m/A) and (0.05, 0.1 · 10−3 m/A) for MD. The curves are mean gi values of the model runs, and the length of the error bars is two standard deviations.
4.2.6. Concentration of SP Particles
 A broad distribution of particle sizes was inferred for the SP grains based on frequency dependence of susceptibility across the whole spectrum of measurement temperatures (Figure 6a). This implies that the χSP value to be used in equation (11) for the calculation of fSP must be the average of SP susceptibilities over the entire range of SP volumes. We calculate χSP following Worm , which assumes even coercivity distributions between 40 and 60 mT for of each grain size fraction. For a measurement frequency of 100 Hz, average χSP across the frequency-dependence interval is 4 · 10−3 m3/kg. χnonSP was calculated using an SD value of 0.4 · 10−3 m3/kg, and an MD value of 0.6 · 10−3 m3/kg (average values for nonstoichiometric magnetite [Dunlop and Özdemir, 1997]), weighed by their respective fractions as obtained from system (9). SP fraction fSP is plotted in Figure 6b (continuous line); Unit 1 SP fractions are between 0.05 and 0.1, while Unit 2 values are in the interval 0.1–0.2. For comparison, dashed lines are fSP curves calculated using χSP values of 3 · 10−3 m3/kg (higher values), and 5 · 10−3 m3/kg (lower values). Figure 6c illustrates the contributions of the SP and non-SP fractions to χferri. The SP particles account for as much as 50% of χferri in some intervals, even though their concentration is only ∼10%.The non-SP baseline in Unit 1 has slightly higher values than in Unit 2 because of the prevalence of MD particles, but the average baseline value is equivalent to the one used by Hunt et al. [1995b]. Support for our method is provided by the Mössbauer analysis of the magnetic extract. The SP concentration given by the narrow Fe3+ doublet in Figure 4c (representing paramagnetic and SP iron oxides) is 12% of the ferrimagnetic material (9% of total Fe). Given that not only ferrimagnetic SP material contributes to this doublet, this value should be taken as a maximum SP concentration. By comparison, our ferrimagnetic SP fraction calculation for the top 10–15 cm of the core (equivalent to the surface sample from which the extract was prepared) yields an average concentration of 8%.
4.2.7. Ferrimagnetic Flux Model
 In the previous sections we have calculated the mass of ferrimagnetic material relative to the total dry sediment mass (Figure 4d), and the partition between its constituent components: UNISD, ISD, MD (Figure 5c), and SP (Figure 6b). Knowing the pre- and post-settlement sedimentation rates from the Brownie Lake age model [Swain, 1984], sediment density from core logging, and composition from LOI, the calculated mass fractions of the ferrimagnetic components can be expressed as sediment loads or fluxes (Figure 7) according to equations (7) and (8). The full interpretation of the temporal fluctuations of the ferrimagnetic components in terms of regional environmental and anthropogenic forcing factors will be discussed in detail elsewhere (I. Lascu et al., manuscript in preparation, 2010); however, a synopsis follows. The annual sedimentary ferrimagnetic flux before European settlement is fairly constant at 0.01–0.02 mg/cm2, and is dominated by the SD and SP fractions (∼70%). After 1850 the total flux steadily increases and by 1950 is an order of magnitude higher than in pre-settlement times. This tenfold increase is observed in the MD, ISD, and SP components. The 1917 lake level lowering is marked by short-lived abrupt increase in sediment delivery from the surrounding catchment, marked in Figure 7 by peaks in the MD and ISD components. The annual UNISD flux is on the order of 2–6 μg/cm2 before, and 4–12 μg/cm2 after settlement, with the lowest values (<2 μg/cm2) occurring in the eighteenth and nineteenth centuries. By comparison to the other components, whose fluxes are controlled by increased erosion rates, UNISD post-settlement values are only two times higher than in pre-settlement times, and are tied to an increase in nutrient delivery brought by anthropogenically driven eutrophication of the lake in the twentieth century [Swain, 1984]. The low UNISD values that predate the 1917 lake level lowering are interpreted as a sign of the reductive dissolution front migrating downward into the sediment column after the establishment of meromictic conditions.
4.3. Discussion of Modeling Parameters Selection
 We here focus on the significance of the choice of modeling parameters in understanding ferrimagnetic components in their sedimentary context. The total ferrimagnetic mass calculation is based on Ms, an intrinsic property of ferromagnetic materials [Dunlop and Özdemir, 1997]. The error associated with fferri (or cferri) is strictly related to the determination of ferrimagnetic mineralogy, and has a maximum value of 19% in the general case of non-stoichiometric magnetite (i.e., unknown oxidation parameter z). To decrease this error, low temperature magnetization curves and Mössbauer 57Fe spectroscopy have been employed to narrow down possible z values for each of sedimentary unit. The low temperature magnetic behavior of Unit 1 samples and the Mössbauer analysis of the surface sample indicate that the magnetite is only oxidized at the particle surface. Brownie Lake has been meromicitic since the 1920s, having anoxic and reducing bottom waters that are rich in dissolved Fe2+ and Mn2+ [Swain, 1984; Tracey et al., 1996], an unfavorable environment for oxidation of magnetite particles. On the contrary, reductive dissolution can potentially remove SP nanoparticles and reduce the size of SD grains to SP [Anderson and Rippey, 1988; Tarduno, 1995; Geiss et al., 2004]. The magnetite particles must either have been already oxidized before deposition and have survived without being completely reduced, or underwent oxidation during the laboratory storage period of the core and samples, between collection and measurement. Before settlement, the lake water was only seasonally anoxic, complete mixing of epilimnetic and hypolimnetic waters occurring at spring and fall turnover events. Evidence for this can be inferred from the lake's reduced relative depth, the absence of annually laminated sediments, higher sedimentary Fe/Mn ratio, and the presence of a diatom flora in a higher-trophic status [Swain, 1984; Tracey et al., 1996]. Because of the more oxic conditions, and of the one order of magnitude lower sedimentation rate [Swain, 1984], Unit 2 ferrimagnetic particles are in a more advanced oxidation state. The average magnetic grain size is also lower than in Unit 1, which means an increased surface-to-volume ratio, making the grains more susceptible to oxidation. The choice of μferri for each unit was therefore determined by a combination of sediment-magnetic characteristics and evidence of limnological conditions at the time of deposition.
 The remanence-carrying components have been modeled by way of a three-component mixing model, using specific end-member values for remanence and ARM ratios. According to our model, bulk Mrs/Ms and χa/Mrs of a sample can be translated into mass fractions for each component considered, here UNISD, ISD and MD. The basis for defining these particular components is the ability of the two ratios to discriminate between grain-size categories (Mrs/Ms) and inter-particle interactions (χa/Mrs). A judicious choice of end-member ratios will result in lower model errors. The components for Brownie Lake were defined with the knowledge that lake sediments in temperate-climate areas are characterized by a mixture of detrital and endogenic magnetic particles [Snowball et al., 2002; Geiss et al., 2003; Egli, 2004], and that nonstoichiometric magnetite is the ferrimagnetic carrier in our sediments. The detrital fraction is generally dominated by MD particles, but can also contain finer SD and SP grains (e.g., of pedogenic origin). The MD component sensu stricto (no PSD grains) has low remanence and ARM ratio values (Mrs/Ms < 0.05, χa/Mrs ∼ 0.1 · 10−3 m/A). A PSD end-member would have a higher remanence ratio (e.g., 0.2 for 1 μm grains), but a similar ARM ratio. We use the cutoff Mrs/Ms value of 0.05 [Day et al., 1977; Dunlop, 2002] as an average in our model, in order to incorporate the effects of both true MD and PSD grains. This value corresponds to an average grain size of ∼20 μm [Yu et al., 2002]. The 0.01 Mrs/Ms value used in the error estimation for the MD component (g3 in Figure 5c) corresponds to much larger particles (∼100–200 μm) [Day et al., 1977; Dunlop, 2002], and would be a limit case. The detrital SD grains can be transported into a depositional basin either independently through sorting, or in most cases as part of clay/organic matter aggregates that also contain larger ferrimagnetic particles. In both situations the SD particles are disturbed to a certain extent from their original configuration (e.g., dispersion in a soil matrix). It is then reasonable to assume that they contribute to both ISD and UNISD end-members. The ISD component is characterized by SD-like remanence ratios, and MD-like ARM ratios, and was defined to represent the extreme case of strong interactions between SD particles clumped in aggregates [Moskowitz et al., 1993; Kopp et al., 2006]. Both detrital (e.g., pedogenic) and endogenic (biogenic and inorganic) SD particles that occur in such closely packed configurations are expected to contribute to ISD. The UNISD component is designed to include only isolated grains or undisturbed linear chains of bacterial magnetosomes [Yamazaki, 2008; Egli et al., 2010]. The remanence ratio for magnetite UNISD particles is 0.5 by definition [Stoner and Wohlfarth, 1948]. For greigite magnetosomes the remanence ratio usually exceeds 0.5, approaching a theoretical value of 0.83 as Hcr/Hc approaches unity, due to a  easy axis of magnetization and the prevalence of magnetocrystalline anisotropy over shape anisotropy [e.g., Roberts, 1995; Sagnotti and Winkler, 1999; Chang et al., 2009]. The ARM ratio of UNISD can be determined with the help of coercivity deconvolution of samples harvested from the OAI, by calculating the ARM ratio of the biogenic coercivity-spectrum component (3.5 · 10−3 m/A in our model). The biogenic component defined by its coercivity is likely to include interacting particles from magnetosome clusters and bundled or collapsed chains [Egli et al., 2010], which can artificially lower (χa/Mrs)UNISD. On the other hand, the detrital coercivity-spectrum component may include non-interacting particles with lower initial ARM ratios (e.g., 1–3 · 10−3 m/A for pedogenic particles [Egli, 2004; Geiss et al., 2008]), which should truly lower (χa/Mrs)UNISD. Our error estimation for the UNISD end-member (g1 in Figure 5c) was based on ARM ratios in the interval 3–4 · 10−3 m/A. The error is higher for Unit 2 samples, indicating that the choice of ARM ratio for the UNISD component is more critical for finer grained magnetic assemblages.
 The SP component fraction is modeled using the ferrimagnetic susceptibility χferri (derived from χf/Ms) by subtracting the non-SP baseline susceptibility [Hunt et al., 1995b]. The critical parameter in the calculation of fSP is the susceptibility of the SP ferrimagnetic grains, which can vary over an order of magnitude with SP grain size [Worm, 1998]. Frequency-dependent susceptibility measurements across a range of temperatures are therefore necessary to characterize the SP particle size distribution, as a preliminary step for calculating a representative χSP. Sediments usually comprise magnetic particles characterized by a wide grain-size distribution in the SP realm [Dearing et al., 1996], so an average χSP value calculated over the SP size spectrum is a reasonable assumption in most cases. This approach is preferred to the traditional room temperature susceptibility measurements at two frequencies (χfd parameter), which captures only a narrow interval of the grain-size distribution curve.
 1. We provide a quantitative model for calculating the concentrations of ferrimagnetic sedimentary components using rock magnetic properties. The quantification method is based mainly on bulk room temperature measurements, and translates raw magnetic parameters into ferrimagnetic mass concentrations. This method eliminates dilution effects on magnetic properties by weakly magnetic substances in high concentrations, such as water, organic matter, carbonates, clay minerals, etc., and allows the calculation of ferrimagnetic particle fluxes for dated sedimentary sequences. It can be applied for reconstructing past environmental changes in a range of sedimentary environments, and is particularly useful for large sets of samples, where detailed magnetic unmixing methods (especially low-temperature techniques) are unfeasible due to time or instrument constraints.
 2. Total ferrimagnetic concentration is most accurately determined from in-field magnetization measurements. Saturation magnetization corrected for non-ferrimagnetic contributions (Ms) is the most reliable parameter, only ferrimagnetic mineralogy being needed for concentration calculations. Susceptibility-based concentrations are less reliable because they require a priori knowledge about ferrimagnetic grain size and shape in addition to magnetic mineralogy. Remanence measurements are useful as concentration proxies only when magnetic composition is uniform with respect to mineralogy and grain size, due to the varying degree of remanence acquisition efficiency for different categories of magnetic particles.
 3. Anhysteretic and saturation isothermal remanences are used here to model the concentrations of the remanence-carrying ferrimagnetic fractions via a three-component mixing model, which is tested on mixtures of SD and non-SD magnetite grains of known concentrations. The use of the ARM ratio (χa/Mrs) as a proxy for inter-particle magnetostatic interactions allows the separation of SD particles into two separate components (UNISD and ISD), which may have independent origins. The remanence ratio (Mrs/Ms) is a true grain-size indicator, whereas χa/Mrs should be used in that capacity only when the proportion of interacting particles is constant.
 4. For a robust quantification of the superparamagnetic fraction, we propose a technique that corroborates ferrimagnetic susceptibility calculations with information about the SP particle size distribution obtained from the frequency and temperature dependence of magnetic susceptibility. This approach is recommended, when possible, in lieu of frequency-dependent susceptibility measurements at room temperature only.
 We thank the National Lacustrine Core Repository (LacCore) at the University of Minnesota for access to the Brownie Lake core and initial description data, Amy Chen for help with water sampling and filtering, Bruce Moskowitz and Brian “The Dude” Carter for access to the synthetic mixtures. Mike Jackson's comments and suggestions significantly improved the development of our methodology. Constructive reviews by Christoph Geiss, Mike Jackson, Leonardo Sagnotti and an anonymous referee have helped improve this manuscript. I.L. has benefited from the support of a University of Minnesota Doctoral Dissertation Fellowship. The Institute for Rock Magnetism is funded by the National Science Foundation, the Keck Foundation, and the University Of Minnesota. This is IRM contribution 1003.